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1.
Lunar physical librations and laser ranging   总被引：1，自引：0，他引：1  
The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured, in addition to and, by laser ranging to the Moon. Combining the laser ranging determinations of = 630.6 ± 0.5 × 10–6 and = 226.4 ± 3.0 × 10–6 with lunar orbiter measurements ofC 20 andC 22 givesC/MR 2=0.395 -0.010 +0.006 . Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.Communication presented at the Conference on Lunar Dynamics and Observational Coordinate Systems, held January 15–17, 1973, at the Lunar Science Institute, Houston, Tex., U.S.A.  相似文献   

2.
The parameters of the best-fitting ellipsoid have been derived using the latest spherical harmonics of the Phobos topography (Duxbury, 1989) by solution of non-linear overdetermined inverse problem. The lengths of the equatorial axes of the ellipsoid have been determined (a = 12.9 km, b = 11.4 km). They are nearly the same as established by Duxbury (ibid.) on the basis of the linearized relationship between the squared lengths of ellipsoidal axes and the topography coefficients C 20 and C 22. The length of the polar axis (c = 9.1 km) differs of about 20% from Duxbury's value. Supposing mass homogeneity of Phobos, the Stokes parameters of the external gravitational field have been derived up to those of the sixth degree and order. The large irregularities in the Phobos figure cause the values of the Duxbury's potential coefficients be fairly inaccurate except the harmonics C 20, C 32, S 43 and S 51, i.e. linearized relationship between gravity and topography cannot be applied for Phobos. Finally, positions of the centre of figure and the directions of the principal axes of inertia have been established.  相似文献   

3.
Density models for the Moon, including the effects of temperature and pressure, can satisfy the mass and moment of inertia of the Moon and the presence of a low density crust indicated by the seismic refraction results only if the lunar mantle is chemically or mineralogically inhomogeneous. IfC/MR 2 exceeds 0.400, the inferred density of the upper mantle must be greater than that of the lower mantle at similar conditions by at least 0.1 g cm–3 for any of the temperature profiles proposed for the lunar interior. The average mantle density lies between 3.4 and 3.5 g cm–3, though the density of the upper mantle may be greater. The suggested density inversion is gravitationally unstable, but the implied deviatoric stresses in the mantle need be no larger than those associated with lunar gravity anomalies. UsingC/MR 3=0.400 and the recent seismic evidence suggesting a thin, high density zone beneath the crust and a partially molten core, successful density models can be found for a range of temperature profiles. Temperature distributions as cool as several inferred from the lunar electrical conductivity profile would be excluded. The density and probable seismic velocity for the bulk of the mantle are consistent with a pyroxenite composition and a 100 MgO/(MgO+FeO) molecular ratio of less than 80.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.  相似文献   

4.
Dense Doppler tracking coverage of the Apollo 15 and 16 subsatellites over ten and eighteen day periods when periapsis altitudes were 15–50 km has provided detailed gravity mapping of the lunar frontside. Many new gravity features are revealed including one that does not correlate with any visible topographic structure. All unfilled craters sampled are negative anomalies. The mascons consistently produce gravity highs that load the surface with ≈800 kg cm?2 excess mass. The Orientale region is represented with a solution grid of 177 point masses that clearly show the ringed structure. The eastern limb is also displayed with a solution grid of point masses. The gravity variations over the central portion of the frontface are shown as line-of-sight acceleration contours in milligals.  相似文献   

5.
A global lunar topographic map has been derived from existing Earth-based and orbital observations supplemented in areas without data by a linear autocovariance predictor. Of 2592 bins, each 5° square, 1380 (64.7% by area) contain at least one measurement. A spherical harmonic analysis to degree 12 yields a mean radius of 1737.53 ± 0.03 km (formal standard error) and an offset of the center of figure of 1.98±0.06 km toward (19±2)°S, (194±1)°E. A Bouguer gravity map, derived from a 12-degree free-air gravity model and the present topography data, is presented for an elevation of 100 km above the mean surface. It is confirmed that the low-degree gravity harmonics are determined primarily by surface height variations and only secondarily by lateral density variations.  相似文献   

6.
Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W 0 = (12,654,875 ± 69) (m2/s2), is used as one of the four fundamental gravity parameters of Mars namely, {W 0, GM, ω, J 20}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.  相似文献   

7.
In the present article models of well behaved charged superdense stars with surface density 2×1014 gm/cm3 are constructed by considering a static spherically symmetric metric with t = const hypersurfaces as spheroids and hyperboloids. Maximum mass of the star is found to be 7.66300M Θ with radius 19.35409 km for spheroids case while 1.51360M Θ with radius 13.72109 km for hyperboloid case satisfying ultra-relativistic conditions. The solutions thus found satisfy all the reality and causality conditions. For brevity we don’t present a detailed analysis of the derived solutions in this paper.  相似文献   

8.
In the gravity field of an asteroid with the second order and degree harmonics C 20 and C 22, the attitude stability of a spacecraft with two flexible solar arrays on a stationary orbit subjected to the fourth-order gravity gradient torque is investigated in this paper. The sufficient conditions of attitude stability of the spacecraft are obtained, the effect of the direction of the flexible solar arrays and some special cases are discussed. Taking the asteroids 4769 Castalia, 25143 Itokawa and the imaginary asteroids as examples, the attitude stability domains, determined by the sufficient conditions, of the spacecrafts moving on stationary orbits around them are presented. It is found that the attitude stability domains of the spacecraft with two flexible solar arrays are evidently different when the solar arrays are installed in different directions; the effect of the harmonics C 20 and C 22 of the asteroids has the significant influence on the attitude stability domains of the spacecrafts with flexible appendages moving on stationary orbits; in the certain case, the effect of the harmonics C 20 and C 22 of the asteroids has no influence on the attitude stability domains of the rigid spacecrafts moving on stationary orbits, but in the other cases, the effect of the harmonics C 20 and C 22 of the asteroids has also the significant influence on the attitude stability domains of the rigid spacecrafts moving on stationary orbits; whether the harmonics C 20 and C 22 of the asteroids are considered or not, the effect of flexible appendages decreases the attitude stability domains.  相似文献   

9.
In the present article a model of well behaved charged superdense star with surface density 2×1014 gm/cm3 is constructed by considering a static spherically symmetric metric with t=const hypersurfaces as hyperboloid. So far well behaved model described by such metric could not be obtained. Maximum mass of the star is found to be 0.343457M ⊙ and the corresponding radius is 9.57459 km. The red shift at the centre and on the surface are given as 0.068887 and 0.031726 respectively.  相似文献   

10.
The order of magnitude of the error is investigated for a first-order von Zeipel theory of satellite orbits in an axisymmetric force field, i.e., first-order long period and short-period effects are included along with second order secular rates. The treatment is valid for zero eccentricity and/or inclination. In the case where initial position and velocity vectors are known, the in-track position error over time intervals of order 1/J 2 is kept at 0(J 2 2), like the other position errors and velocity errors, by calibration of the mean motion with the aid of the energy integral. The results are specifically applicable to accuracy comparisons of the Brouwer orbit prediction method with numerical integration. A modified calibration is presented for the general asymmetric force field which includes tesseral harmonics.  相似文献   

11.
In the present article, a family of static spherical symmetric well behaved interior solutions is derived by considering the metric potential g 44=B(1−Cr 2)−n for the various values of n, such that (1+n)/(1−n) is positive integer. The solutions so obtained are utilised to construct the heavenly bodies’ like quasi-black holes such as white dwarfs, neutron stars, quarks etc., by taking the surface density 2×1014 gm/cm3. The red shifts at the centre and on the surface are also computed for the different star models. Moreover the adiabatic index is calculated in each case. In this process the authors come across the quarks star only. Least and maximum mass are fond to be 3.4348M Θ and 4.410454M Θ along with the radii 21.0932 km and 23.7245 km respectively.  相似文献   

12.
The canonical equations of motion of an artificial lunar satellite are formulated including the effects of the asphericity of the Moon comprising the harmonics J 2, J 22, J 3, J 31, J 4 andJ 5, the oblateness of the Earth up to the second zonal harmonic, as well as the disturbing function due to the attractions of the Earth and of the Sun (terms are retained up to order 10-6 for the higher orbits and 10-8 for the lower orbits). This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

13.
First ever closed form solution for charged fluid sphere expressed by a space time with its hypersurfaces t= constant as spheroid is obtained for the case 0<K<1. The same is utilized to construct a superdense star with surface density 2×1014 gm/cm3. The star is seen to satisfy the reality and causality conditions for 0<K≤0.045 and possesses maximum mass and radius to be 0.065216M Θ and 1.137496 km respectively. Moreover the interior of the star satisfy strong energy condition. However in the absence of the causality condition, the reality conditions are valid for a wider range 0<K≤0.13. The maximum mass and radius for the later case are 1.296798M Θ and 2.6107 km respectively for the strong energy condition, while the said parameters for the weak energy condition read as 1.546269M Θ and 2.590062 km respectively.  相似文献   

14.
Doppler tracking data from the Pioneer Venus Orbiter (PVO) have been used to estimate the anomalous gravity field in the region of Venus west of Beta Regio. The analysis invokes a Kalman filter-smoother to solve the nonlinear spacecraft state estimation problem and a linear Bayesian estimator to perform the geophysical inversion. The topographic map for this region, derived from the PVO radar, has been filtered to have the same distortions and degree of smoothing as the gravity map. The undulations of the gravity are about 0.2 times as large as expected from the topography on the assumption that the latter is uncompensated. A comparison of the gravity and topography by means of the spectral admittance is consistent with Airy compensation at a depth of 50 km if the surface material has a density of 2.6 g/cm3. However, this is not a unique interpretation.  相似文献   

15.
Conspicuous excess brightness, exceeding that expected from coronal and zodiacal light (CZL), was observed above the lunar horizon in the Apollo 15 coronal photographic sequence acquired immediately after orbital sunset (surface sunrise). This excess brightness systematically faded as the Command Module moved farther into shadow, eventually becoming indistinguishable from the CZL background. These observations have previously been attributed to scattering by ultrafine dust grains (radius ∼0.1 microns) in the lunar exosphere, and used to obtain coarse estimates of dust concentration at several altitudes and an order-of-magnitude estimate of ∼10−9 g cm−2 for the column mass of dust near the terminator, collectively referred to as model “0”.We have reanalyzed the Apollo 15 orbital sunset sequence by incorporating the known sightline geometries in a Mie-scattering simulation code, and then inverting the measured intensities to retrieve exospheric dust concentration as a function of altitude and distance from the terminator. Results are presented in terms of monodisperse (single grain size) dust distributions. For a grain radius of 0.10 microns, our retrieved dust concentration near the terminator (∼0.010 cm−3) is in agreement with model “0” at z=10 km, as is the dust column mass (∼3–6×10−10 g cm−2), but the present results indicate generally larger dust scale heights, and much lower concentrations near 1 km (<0.08 cm−3 vs. a few times 0.1 cm−3 for model “0"). The concentration of dust at high altitudes (z>50 km) is virtually unconstrained by the measurements. The dust exosphere extends into shadow a distance somewhere between 100 and 200 km from the terminator, depending on the uncertain contribution of CZL to the total brightness. These refined estimates of the distribution and concentration of exospheric dust above the lunar sunrise terminator should place new and more rigorous constraints on exospheric dust transport models, as well as provide valuable support for upcoming missions such as the Lunar Atmosphere and Dust Environment Explorer (LADEE).  相似文献   

16.
On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C2,2, is well determined and correlates with the equatorial shape. The S2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J2, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (Cm/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.  相似文献   

17.
The precision of lunar gravity field estimation has improved by means of three to five orders of magnitude since the successful GRAIL lunar mission. There are still discrepancies however, in the low degree coefficients and long wavelength components of the solutions developed by two space research centers (JPL and GSFC). These discrepancies hint at the possibilities for improving the accuracy in the long wavelength part of the lunar gravity field. In the near future, China will launch the Chang’E-5 lunar mission. In this sample-return mission, there will be a chance to do KBRR measurements between an ascending module and an orbiting module. These two modules will fly around lunar at an inclination of ～49 degrees, with an orbital height of 100 km and an inter-satellite distance of 200 km. In our research, we simulated the contribution of the KBRR tracking mode for different GRAIL orbital geometries. This analysis indicated possible deficiencies in the low degree coefficient solutions for the polar satellite-to-satellite tracking mode at various orbital heights. We also investigated the potential contributions of the KBRR to the Chang’E-5 mission goal of lunar gravity field recovery, especially in the long wavelength component. Potential improvements were assessed using various power spectrums of the lunar gravity field models. In addition, we also investigated possible improvements in solving lunar tidal Love number K2. These results may assist the implementation of the Chang’E-5 mission.  相似文献   

18.
Slitless spectrograms of the chromosphere obtained during the eclipse of 4–5 February 1962 have been analyzed to obtain the decrements of the level populations of hydrogen, the self-absorption in the Balmer lines, and parameters useful in construction of models of the low chromosphere.The decrement of the high energy levels of hydrogen inferred under the optically thin assumption does not vary significantly with height, and it appears to be unnecessary to seek large deviations from local thermodynamic equilibrium in the high levels. The observed Balmer-to-Paschen line intensity ratios have been used to infer self-absorption and opacities in the Balmer lines. The resulting population of the second energy level is about an order of magnitude smaller than that found by Athay and Thomas from the 1952 data.The chromospheric continuum was generally underexposed; the absence of observed continuum in the visible region of the spectrum made it impossible to derive a unique model from the 1962 data alone. However, the high Balmer line data and new theoretical solutions of the statistical equilibrium equations for hydrogen combined with corrected 1952 observations at 4700 A are compatible with a model having approximately the same temperature and neutral hydrogen structure as the 1952 model by Pottasch and Thomas but half the electron density: T e = 6200K, N 1 = 7.4 × 1013 cm-3, N e = 2.3 × 1011 cm-3 at 500 km and T e = 7200K, N 1 = 2.6 × 1012 cm-3, N e = 1.7 × 1011 cm-3 at 1000 km.Based in part on a Ph.D. thesis submitted to the Department of Astro-Geophysics, University of Colorado.Now at the Department of Astronomy, Indiana University.  相似文献   

19.
TheS-Band Transponder experiment used precision doppler tracking data of the command and service module, the lunar module and the subsatellite to provide detailed information about the near side gravity field. No special instruments are required other than the existingS-Band transponder used for real time navigation. The data consists of variations in the spacecraft speed as measured by the earth-based radio tracking system, which has a resolution of 0.65 mm/s.Initial data reduction has been concentrated on the low altitude CSM data ( 20 km) which provides new detailed gravity profiles of the Serenitatis and Crisium mascons. The results are in good agreement with Apollo 14 analysis and strongly suggest that the mascons are near surface features with a mass distribution per unit area of approximately 800 kg/cm2. The Apennines reveal themselves as a local gravity high of 85 mgal and Marius Hills likewise have a gravity high of 62 mgal.The subsatellite data is too sparse at present to definitely determine new gravity anomaly locations. The spacecraft is functioning well and a dense data block is being obtained, which will provide a new gravity map from ±95° longitude to ±30 latitude. Since periapsis altitudes are following relatively close to predicted altitudes, it seems fairly safe at this point to believe the subsatellite lifetime will be at least one year.  相似文献   

20.
Magnetometer data obtained during the first four lunations after the deployment of the Apollo 15 subsatellite have been used to construct contour maps of the lunar magnetic field referred to 100 km altitude. These contour maps cover a relatively small band on the lunar surface. Within the region covered there is a marked near side-far side asymmetry. The near-side field is generally weaker and less structured than the far-side field. The strongest intrinsic lunar magnetic field detected is between the craters Van de Graaff and Aitken, centered at 20°S and 172°E. The variation in field strength with altitude for this feature suggests that its scale size is on the order of 80 km. A magnetization contrast between this region and its surroundings of the order of 6 × 10–5 emu-cm–3 is obtained assuming a 10-km thick slab. Preliminary Apollo 16 magnetometer data at extremely low altitude (0 to 10 km) show a very structured magnetic field with field strengths up to 56. Large compressions in the magnetic field magnitude, just above the lunar limb regions, are occasionally detected when the Moon is in the solar wind. The occurrence of limb compressions is strongly dependent on the selenographic coordinates of the lunar region on the solar wind terminator beneath the orbit of the sub-satellite. The discovery of remanent magnetization of varying strength over much of the lunar surface and its correlation with limb compression source regions supports the hypothesis that limb compressions are due to the deflection of the solar wind by regions of strong magnetization at the lunar limbs. If this hypothesis is correct, then the map of lunar regions associated with compressions indicates that the northerly equatorial region on the far side is less strongly magnetized than the southerly equatorial region on the far side.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.  相似文献   

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